(a) Show that the set of all positive rational no.'s is a countably i…

Previous year question for Discrete Mathematics.

Question

(a) Show that the set of all positive rational no.'s is a countably infinite set.

(b) Show that the function $f: \mathbb{R} \to \mathbb{R}$ define by $f(x) = 2x^3 + 1$, $\forall x \in \mathbb{R}$ is a bijection.

(c) Determine the no. of integers between 1 and 250 which are divisible by any of the integers 2, 3, 5, 7.

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